Abbottsville, a medium sized suburban community, has seen a steady increase in its population over the past 15 years. In 1995, the population was around 25,000. The population has increased at a rate of about 1,000 people per year since then. The graph below shows the trend described above. Use the graph to answer the following question:

If the trend continues as shown, what is the expected population of Abbottsville in 2015?

A
45,000

B
41,000

C
40,000

D
50,000

Let's call 1995 year 0, and at year 0, the population was 25000. The coordinate for this is (0, 25000). If the population has increased at a rate of 1000 people per year, that is the slope of the line. (Normally, population growth is exponential. But since our growth was given as an increase in people as a number as opposed to the increase in people as a percentage, this is linear.)

We will use the point-slope form of a line to write the model for this situation, then use the model to answer the question.

y - 25000 = 1000(x - 0) and

y = 1000x + 25000

Going back to the fact that 1995 is year 0, that makes 2015 year 20. We will sub in a 20 for x to solve for y, the population expected in the year 2015:

y = 1000(20) + 25000 and

y = 20000 + 25000 so

y = 45000

Approximately 45000 people in the year 2015, choice A.